Find the number(s) b such that the average value of on the interval [0, b] is equal to 6. f(x) = 6x² - 54x + 97

Q: Find the right match for the following ODEs in the dropdown menu y' = y" JS sin(x) 5xy' = y - 3x²y"…

A: This is a problem related to differential equation. Please find the answer as below.

Q: a. b. n=1 8 n någn-1 (-5)n 1 nVn? +1

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A: The equation is given by x+y3-100y=7                         ..........(1) To evaluate: (a) All…

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Q: y" +1²y=0, 0<x< 1 2y (0) + y (0) = 0 y(1) 0

A: Please find the detailed answer in the image attached.

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A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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Q: Evaluate the limit using L'Hopital's rule. Enter either a reduced fraction or DNE. lim 7…

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Q: Find the limit. lim X→1 lim X→1 √√x² +15-4 2 X-1 2 x + 15 -4 X-1 || = (Type an integer or a…

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Q: (1 + y²) dx + (x²y + y) dy = 0.

A: The differential equation is given by 1+y2dx+x2y+ydy = 0                               ........1 To…

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Q: Consider the function f(x) = 2x³ 12x² 30x + 7 on the interval [-4, 7]. Find the average or mean…

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Q: (b) Determine whether the series Σ n=1 5n cos(3n) 2en converges or diverges.

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Q: If f(x) = 4 cos(2 ln(x)), find ƒ'(x). Find f'(5) rounded to 3 decimal places.

A: Given function f(x)=4cos(2ln(x))

Q: 4. I Find the general solution of the given system: dx1 dt dx2 dt = 7x1 +4x₂2 =-3x1-x2

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Q: For the given cost function C(x) = 19600 + 200x + x² find: a) The cost at the production level 1750…

A: Since, you have posted a question with multi-parts. As per guidelines we'll solve only first three…

Q: Find the constants a and b such that the function is continuous on the entire real line. 7₁ ax+b,…

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Q: Evaluate [C 02 6 3 10 160xy³ dydx

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Q: drawing the slope field for the differential equation , I would place slope lines of _________ at…

A: We have to find the required

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Q: If A and B are square matrices of the same size, then it is always the case that AB=BA.

A: Disclaimer: “Since you have asked multiple questions, we will solve the first question for you. If…

Q: (a) Consider the boundary value problem (BVP) y" - 49y=tan(7x), y(0) = 0, y(n/7) = 1. Does this BVP…

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Q: Express the equation in logarithmic form: (a) 45 = 1024 is equivalent to log4 A = B. A = and B = (b)…

A: This question is related to logarithmic equations, we will solve it using given information.

Q: For this week's discussion, you are asked to generate a continuous and differentiable function f(z)…

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Q: 5. Hance sits at one of the points on the curve y = 2x³ -3x²-12x +20 where the tangent is parallel…

A: Please see the below picture for detailed solution.

Q: 2π 12171710727 17/1xsin nx dx 2π I need to solve the integration in a table or zero method, a…

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Q: [ (x − 7) sin(x) dx

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Q: 9) Erin goes for her daily run. The elevation changes, so she can run some sections faster than…

A: Given

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A: Given 1. A license plate must contain 2 numerical digits followed by 2 letters. 2. the first digit…

Q: Use linear approximation, i.e. the tangent line, to approximate √49.4 as follows: Let f(x)=√x. Find…

A: For function, f  the linear approximation at a is given by L(x)=f(a)+f'(a)(x-a)   ...............(1)…

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Q: Question Find the change in surface area dA if the radius of a sphere changes from 11 cm to 10.8 cm.…

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Q: Use integration by parts to evaluate the definite integral fr² ln x dr

A: Topic- integration by parts

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A: Given:        ∫∫Rx2+ydA=∫12∫02πr2cos2θ+rsinθrdθdr…

Q: π f(x,y) = sin 3(x+y) over the square 0≤x≤60sys 6. R

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Q: Match equation question type with a graph - y= Ⓒy= + Ⓒy= y= x-A x-B x-A (x-B)² (x - A)² x-B (x - A)²…

A: Given data:- In the given question four different equations will be given and find out which graph…

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A: Given that,            The solid is obtained by rotating the region bounded by the given curves…

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Q: 5. Use the definition of a Maclaurin Series to express f(2) = as a Power Series. Give the 8th degree…

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Q: Use the definition of Taylor series to find the Taylor series, centered at c, for the function. f(x)…

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Q: True or False? Let R be a ring and a, be R. Then a^2 - b^2 = (a-b (a+b) v a,b € R

A: We can check that the given statement is true or false.

Q: 8] n=1 1 n√n +1

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Q: Find lim a. lim x→0* c. lim x²- - 5x + 6 2 3 x - 3x x -5x+6 b. lim x+3+ x³-3x² 2 x -5x+6 x³ - 3x² X…

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Q: Determine which of the following power series is equal to the function f(x) = -V2<<√2 0 0 n=0 IM IM…

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